A273670 Numbers with at least one maximal digit in their factorial base representation.

1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 75, 76, 77, 79, 81, 82, 83, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105

Offset: 0

Author

Antti Karttunen, May 29 2016

Keywords

• nonn
• base

Comments

Indexing starts from 0 (with a(0) = 1) to tally with the indexing used in A256450.

Numbers n for which is A260736(n) > 0.

Involution A225901 maps each term of this sequence to a unique term of A256450, and vice versa.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A153880 (complement).

Cf. A273663 (a left inverse).

Cf. A260736.

Cf. also A225901, A256450.

Programs

Mathematica

r = MixedRadix[Reverse@ Range[2, 12]]; Select[Range@ 105, Total@ Boole@ Map[SameQ @@ # &, Transpose@{#, Range@ Length@ #}] > 0 &@ Reverse@ IntegerDigits[#, r] &] (* Michael De Vlieger, Aug 14 2016, Version 10.2 *)

Python

from sympy import factorial as f
def a007623(n, p=2): return n if n
0 else '0' for i in x])[::-1]
    return 0 if n==1 else sum([int(y[i])*f(i + 1) for i in range(len(y))])
def a260736(n): return 0 if n==0 else n%2 + a260736(a257684(n))
print([n for n in range(106) if a260736(n)>0]) # Indranil Ghosh, Jun 20 2017

Formula

a(0) = 1, and for n > 1, if A260736(1+a(n-1)) > 0, then a(n) = a(n-1) + 1, otherwise a(n-1) + 2. [In particular, if the previous term is 2k, then the next term is 2k+1, because all odd numbers are members.]

Other identities. For all n >= 0:

A273663(a(n)) = n.